please help me with this homework question

Given a list the functions L you need to re-order them according to the rate of growth from slowest to fastest. Use shorthand f (n) g(n) for f (n) o(g(n)) and f (n) == g(n) for f (n) (g(n)). For example, for functions 2n, n2, log n(n + 1), n(n + 1)

the answer might look like

logn(n+1)n2==n(n+1)2n or logn(n+1)n(n+1)==n22n. You may use the following facts without a proof: 1loglognlognlog2nnnnlognn22nn! Furthermore, for all positive real a and b the following holds: - logano(nb), - nao(bn) for b>1, - and if a